FRBNY - Capital Ratios as Predictors of Bank Failure

8/4/2019 FRBNY - Capital Ratios as Predictors of Bank Failure

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FRBNY EconomicPolicyReview/July2000 33

CapitalRatiosasPredictorsofBankFailure

apitalratios havelong beena valuabletoolforassessingthesafetyandsoundnessofbanks.Theinformaluseof

ratios bybankregulators and supervisors goes backwellovera

century(Mitchell1909).IntheUnitedStates,minimumcapital

ratioshavebeenrequiredinbanking regulation since1981,and

theBaselAccordhas appliedcapitalratiorequirements to

banks internationally since1988.TheBaselCommitteeon

Banking Supervision(1999)is currentlyengagedinaneffortto

improvetheBaselAccordand,onceagain,capitalratios are

being discussedaspartoftheproposed solution.Inthis article,

weexamine someoftheroles thatcapitalratios playinbank

regulationandwearguethat,tobe successfulinanyofthese

roles,capitalratios shouldbeara significantnegativerelation-shiptotheriskofsubsequentbankfailure.Wethenpresent

empiricalevidenceofthoserelationships.

Wefocus hereonthreetypes ofcapitalratiosrisk-

weighted,leverage,andgrossrevenueratios. Foreachratio,we

examinewhatmakes itactuallyorpotentiallyusefulforbank

regulationandweaskwhetheritisindeedsignificantlyrelated

to subsequentbankfailure.Perhaps not surprisingly,wefind

thatallthreeratiosarestronglyinformativeaboutsubsequent

failures.Ouranalysis suggests thatthemostcomplexofthe

ratiostherisk-weightedratiois themosteffectivepredictor

offailureoverlong timehorizons.However,perhaps

somewhat surprisingly,wealsofindthattherisk-weighted

ratiodoes notconsistentlyoutperformthe simplerratios,

particularlywith shorthorizons ofless thantwoyears.Overthe

ArturoEstrellais a senior vice president,SangkyunParkan economist,and

Stavros Peristianiaresearchofficeratthe FederalReserveBankofNewYork.

The authors thankBeverlyHirtle,JimMahoney,Tony Rodrigues,Phil

Strahan,twoanonymous referees,andparticipants inaworkshopatthe

Federal Reserve BankofNew Yorkforhelpful comments and suggestions.The

authorsalsothankGijoonHongfor excellentresearchsupport.The views

expressedarethoseoftheauthors anddonotnecessarilyreflectthepositionof

the Federal Reserve BankofNew Yorkorthe Federal Reserve System.

The current regula tory framework fordetermining bank c apital adequ acy is underreview b y the Basel Committee on B ankingSupervision .

An empirical analysis ofthe relationshipsbetween different capital ratios and bankfailure suggests thattwo simple ratiostheleverage ratio and the ratio of capital to grossrevenuemay m erit a role in the revisedframework.

The leverage ratio and the gross revenue ra tiopredic t bank failure about as well as morecomplex risk-weighted ratios over one- ortwo-ye ar horizons . Risk-weighted ratios tendto perform bett er over longer horizons .

The simple ratios are virtually costless toimplement and could supplement moresophistic ated m easures by providing a timelysignal ofthe need for supervisory ac tion.

Arturo Estrella , Sangkyun Park, and Stavros Peristiani

C


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Table3

DistributionofBankFailures byLeverageRatios

Cutoff

Percentile CutoffPoint

Failures

1989-93

Nonfailures

1989-93

Failur

eRatefor Row

(Percent)

Cumulative Proportion

ofN

on

failur

es(TypeIIError)

(Percent)

Cumulative Proportion

ofFailur

es(TypeIError)

(Percent)

Absolute Scale

0 231 51 81.9 0.1 63.2

1.0 100 62 61.7 0.3 47.3

2.0 90 95 48.6 0.5 33.0

3.0 76 194 28.1 0.9 20.9

4.0 45 367 10.9 1.8 13.7

5.0 31 628 4.7 3.2 8.8

6.0 25 1,799 1.4 7.3 4.8

7.0 17 5,136 0.3 19.1 2.1

8.0 8 8,175 0.1 37.8 0.8

9.0 0 7,767 0.0 55.6 0.8

10.0 3 5,858 0.1 69.0 0.3

11.0 0 3,940 0.0 78.1 0.3

12.0 0 2,702 0.0 84.3 0.3

Infinity 2 6,869 0.0 100.0 0.0

Relative Scale

1 0.97 330 112 74.7 0.3 47.5

2 2.95 166 277 37.5 0.9 21.0

3 4.03 46 397 10.4 1.8 13.7

4 4.78 22 420 5.0 2.8 10.2

5 5.20 13 430 2.9 3.7 8.1

6 5.51 7 436 1.6 4.7 7.0

7 5.75 8 435 1.8 5.7 5.7

8 5.92 3 439 0.7 6.8 5.39 6.06 3 440 0.7 7.8 4.8

10 6.18 2 441 0.5 8.8 4.5

25 7.22 18 6,180 0.3 22.9 1.6

50 8.55 5 11,063 0.0 48.3 0.8

75 10.46 3 11,065 0.0 73.6 0.3

100 Infinity 2 11,508 0.0 100.0 0.0

Sources: Federal FinancialInstitutions ExaminationCouncil,Consolidated Reports ofConditionandIncome;BoardofGovernors ofthe Federal Reserve

System,NationalInformationCenterdatabase;authors calculations.

Notes:Noncumulativedataarefortherangedefinedbycutoffs inthecurrentandtheprevious row.Cumulativedataareaggregateduptothecutoffpoint.


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Table 4

DistributionofBankFailures byGross RevenueRatios

Cutoff


Failures

1989-93

Nonfailures

1989-93

Failure Rate

forRow

(Percent)

CumulativeProportion

ofNonfailures

(TypeIIError)

(Percent)


ofFailures

(TypeIError)

(Percent)

AbsoluteScale

0 231 51 81.9 0.1 63.2

10 102 76 57.3 0.3 47.0

20 93 160 36.8 0.7 32.2

30 75 299 20.1 1.3 20.2

40 42 488 7.9 2.5 13.5

50 36 772 4.5 4.2 7.8

60 13 1,755 0.7 8.3 5.7

70 14 3,634 0.4 16.6 3.5

80 13 5,431 0.2 29.0 1.4

90 5 5,945 0.1 42.6 0.6

100 1 5,431 0.0 55.1 0.5

110 2 4,526 0.0 65.5 0.2

120 0 3,499 0.0 73.5 0.2

Infinity 1 11,576 0.0 100.0 0.0

RelativeScale

1 8.85 323 119 73.1 0.3 48.6

2 25.17 148 295 33.4 0.9 25.0

3 34.56 60 383 13.5 1.8 15.4

4 42.61 24 418 5.4 2.8 11.6

5 47.93 20 423 4.5 3.8 8.4

6 51.97 7 436 1.6 4.8 7.3

7 54.83 4 439 0.9 5.8 6.7

8 57.16 3 439 0.7 6.8 6.2

9 59.09 3 440 0.7 7.8 5.7

10 60.87 2 441 0.5 8.8 5.4

25 75.30 19 6,179 0.3 22.9 2.4

50 94.27 11 11,057 0.1 48.3 0.6

75 120.24 3 11,065 0.0 73.6 0.2

100 Infinity 1 11,509 0.0 100.0 0.0

Sources: Federal FinancialInstitutionsExaminationCouncil,Consolidated ReportsofConditionandIncome;BoardofGovernorso fthe Federal Reserve

System,NationalInformationCenterdatabase;authorscalculations.

Notes:Noncumulative dataare forthe range definedby cutoffsinthe currentandthe previousrow.Cumulative dataare aggregateduptothe cutoffpoint.


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42 CapitalRatiosasPredictorsofBankFailure

thetotalrisk-basedmeasuremaybethemostbindingofall

the FDICIAcapitaladequacyratios.

As expected,theperformanceofcapitalratios deteriorates

somewhatwhenwemovefromaone-yeartoatwo-year

horizon,thatis,whenwefocus onfailures occurring between

oneandtwoyearsafterthecapitalratioisobserved.Tables6-8

summarizethe second-yearfailurerates andcumulative

distributionofsecond-yearfailures andnonfailures forfirms

that survivethefirstyear.Thethreecapitalratios stillprovidea

fairlyclear signal,as evidencedbythe sharpdropinthefailure

Table5

DistributionofBankFailuresbyRisk-WeightedCapitalRatios

Cutoff


Failures

1989-93

Nonfailures

1989-93

Failure Rate

forRow

(Percent)


ofNonfailures

(TypeIIError)

(Percent)


ofFailures

(TypeIError)

(Percent)

Absolute Scale

0 231 52 81.6 0.1 63.2

1.0 69 39 63.9 0.2 52.2

2.0 59 46 56.2 0.3 42.8

3.0 60 73 45.1 0.5 33.3

4.0 55 140 28.2 0.8 24.5

5.0 35 203 14.7 1.3 18.9

6.0 33 261 11.2 1.9 13.7

7.0 25 454 5.2 2.9 9.7

8.0 17 775 2.1 4.7 7.0

9.0 7 1,251 0.6 7.5 5.9

10.0 10 2,217 0.4 12.6 4.3

11.0 5 3,061 0.2 19.6 3.5

12.0 8 3,492 0.2 27.6 2.2

Infinity 14 31,579 0.0 100.0 0.0

RelativeScale

1 1.50 330 112 74.7 0.3 47.5

2 4.31 158 285 35.7 0.9 22.3

3 5.89 51 392 11.5 1.8 14.2

4 6.87 27 415 6.1 2.8 9.9

5 7.55 10 433 2.3 3.8 8.3

6 8.03 8 435 1.8 4.7 7.0

7 8.44 2 441 0.5 5.8 6.7

8 8.77 4 438 0.9 6.8 6.1

9 9.05 1 442 0.2 7.8 5.9

10 9.28 5 438 1.1 8.8 5.1

25 11.42 15 6,183 0.2 22.9 2.7

50 14.66 10 11,058 0.1 48.3 1.1

75 19.86 2 11,066 0.0 73.6 0.8

100 Infinity 5 11,505 0.0 100.0 0.0

Sources: Federal FinancialInstitutionsExaminationCouncil,Consolidated ReportsofConditionandIncome;BoardofGovernorso fthe Federal Reserve


Notes:Noncumulative dataare forthe range definedby cutoffs inthe currentandthe previous row.Cumulative dataare aggregateduptothe cutoffpoint.


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Table6

DistributionofBankFailures byLeverageRatios:Two-Year FailureHorizon

Cutoff


Failures

1989-93

Nonfailures

1989-93

Failure Rate

for Row

(Percent)


ofNonfailures

(Type IIError)

(Percent)


ofFailures

(Type IError)

(Percent)

Absolute Scale

0 24 15 61.5 0.0 94.8

1.0 28 19 59.6 0.1 88.8

2.0 43 36 54.4 0.2 79.6

3.0 44 107 29.1 0.5 70.1

4.0 60 227 20.9 1.2 57.2

5.0 69 428 13.9 2.4 42.4

6.0 71 1,391 4.9 6.4 27.1

7.0 57 4,001 1.4 17.9 14.8

8.0 32 6,627 0.5 37.0 8.0

9.0 9 6,285 0.1 55.1 6.0

10.0 6 4,714 0.1 68.6 4.7 11.0 6 3,242 0.2 78.0 3.4

12.0 5 2,190 0.2 84.3 2.4

Infinity 11 5,462 0.2 100.0 0.0

RelativeScale

1 3.11 154 198 43.8 0.6 66.9

2 4.22 63 289 17.9 1.4 53.3

3 4.93 44 308 12.5 2.3 43.9

4 5.31 25 327 7.1 3.2 38.5

5 5.59 23 329 6.5 4.2 33.5

6 5.80 14 338 4.0 5.1 30.5

7 5.97 13 339 3.7 6.1 27.7

8 6.10 10 342 2.8 7.1 25.6

9 6.22 10 342 2.8 8.1 23.4

10 6.33 8 344 2.3 9.1 21.7

25 7.29 39 4,891 0.8 23.2 13.3

50 8.60 31 8,771 0.4 48.4 6.7

75 10.49 12 8,791 0.1 73.7 4.1

100 Infinity 19 9,135 0.2 100.0 0.0

Sources: Federal FinancialInstitutions ExaminationCouncil,Consolidated Reports ofConditionandIncome;BoardofGovernors o fthe Federal Reserve




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Table7

DistributionofBankFailures byGross RevenueRatios:Two-Year FailureHorizon

Cutoff


Failures

1989-93

Nonfailures

1989-93

Failure Rate

for Row

(Percent)


ofNonfailures

(Type IIError)

(Percent)


ofFailures

(Type IError)

(Percent)

Absolute Scale

0 24 15 61.5 0.0 94.8

10 30 25 54.5 0.1 88.4

20 51 82 38.3 0.4 77.4

30 50 183 21.5 0.9 66.7

40 65 311 17.3 1.8 52.7

50 69 494 12.3 3.2 37.8

60 64 1,183 5.1 6.6 24.1

70 49 2,545 1.9 13.9 13.5

80 25 3,998 0.6 25.4 8.2

90 10 4,628 0.2 38.8 6.0

100 5 4,429 0.1 51.5 4.9

110 3 3,840 0.1 62.6 4.3

120 3 2,988 0.1 71.2 3.7

Infinity 17 10,023 0.2 100.0 0.0

RelativeScale

1 26.19 130 222 36.9 0.6 72.0

2 36.63 69 283 19.6 1.5 57.2

3 44.64 58 294 16.5 2.3 44.7

4 50.08 32 320 9.1 3.2 37.8

5 53.72 21 331 6.0 4.2 33.3

6 56.48 24 328 6.8 5.1 28.2

7 58.90 10 342 2.8 6.1 26.0

8 60.93 15 337 4.3 7.1 22.8

9 62.56 6 346 1.7 8.1 21.5

10 63.99 8 344 2.3 9.1 19.8

25 78.24 49 4,881 1.0 23.1 9.2

50 97.39 19 8,783 0.2 48.4 5.2

75 123.78 8 8,795 0.1 73.7 3.4

100 Infinity 16 9,138 0.2 100.0 0.0

Sources: Federal FinancialInstitutions ExaminationCouncil,Consolidated Reports ofConditionandIncome;BoardofGovernors o fthe Federal Reserve




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Table8

DistributionofBankFailuresbyRisk-WeightedCapitalRatios:Two-Year FailureHorizon

Cutoff


Failures

1989-93

Nonfailures

1989-93

Failure Rate

forRow

(Percent)


ofNonfailures

(TypeIIError)

(Percent)


ofFailures

(TypeIError)

(Percent)

Absolute Scale

0 24 16 60.0 0.0 94.8

1.0 18 10 64.3 0.1 91.0

2.0 22 11 66.7 0.1 86.2

3.0 32 27 54.2 0.2 79.4

4.0 39 68 36.4 0.4 71.0

5.0 34 125 21.4 0.7 63.7

6.0 49 156 23.9 1.2 53.1

7.0 46 306 13.1 2.1 43.2

8.0 58 546 9.6 3.6 30.8

9.0 38 974 3.8 6.4 22.6

10.0 37 1,784 2.0 11.6 14.6 11.0 15 2,533 0.6 18.9 11.4

12.0 10 2,880 0.3 27.2 9.2

Infinity 43 25,308 0.2 100.0 0.0

RelativeScale

1 4.62 150 202 42.6 0.6 67.7

2 6.30 80 272 22.7 1.4 50.5

3 7.15 41 311 11.6 2.3 41.7

4 7.73 34 318 9.7 3.2 34.4

5 8.22 25 327 7.1 4.1 29.0

6 8.58 14 338 4.0 5.1 26.0

7 8.88 14 338 4.0 6.1 23.0

8 9.15 10 342 2.8 7.0 20.9

9 9.35 10 342 2.8 8.0 18.710 9.55 7 345 2.0 9.0 17.2

25 11.52 32 4,898 0.6 23.1 10.3

50 14.66 28 8,774 0.3 48.4 4.3

75 19.73 12 8,791 0.1 73.7 1.7

100 Infinity 8 9,146 0.1 100.0 0.0

Sources: Federal FinancialInstitutions ExaminationCouncil,Consolidated Reports ofConditionandIncome;BoardofGovernors ofthe Federal Reserve




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Table9

LogitRegressionsDependent Variable:FailureinLessThanOneYear

1989

Model1 Model2 Model3 Model4

Intercept -0.0878) -0.2646) -0.3497) -0.0901)

(0.5450) (0.0591) (0.0126) (0.5345)

Leverageratio -77.8819) -74.4450)

(0.0001) (0.0001)

Gross revenue ratio -7.2188) 0.0093)

(0.0001) (0.9588)

Risk-weightedratio, -46.5865) -2.0587)

tier1 (0.0001) (0.6595)

Pseudo-R2 0.1190) 0.1120) 0.1101)) 0.1191))

Concordant(percent) 98.0 97.7 97.0 98.1

Discordant(percent) 1.5 1.7 2.1 1.5

Tie(percent) 0.4 0.6 0.9 0.4

Failures 195

Nonfailures 13,104

1990


Intercept 0.3984) 0.2650) 0.1679) 0.3967)

(0.0179) (0.1007) (0.2992) (0.0182)

Leverage ratio -96.0482) -49.5560)

(0.0001) (0.0194)

Gross revenueratio -10.0654) -5.0353)

(0.0001) (0.0258)

Risk-weightedratio, -58.8834) 0.7287)

tier1 (0.0001) (0.7317)

Pseudo-R2 0.1350) 0.1330) 0.1269) 0.1359)



Tie (percent) 1.2 2.1 1.1 1.6

Failures 161Nonfailures 12,742

1991


Intercept -0.3688) -0.2871) -0.4797) -0.2754)

(0.0260) (0.0781) (0.0034) (0.0939)

Leverageratio -74.3724) -0.4529)

(0.0001) (0.9353)

Gross revenue ratio -8.2146) -8.0113)

(0.0001) (0.0001)


tier1 (0.0001) (0.7826)

Pseudo-R2 0.0790) 0.0756) 0.0648) 0.0757)Concordant(percent) 97.5 97.5 97.4 97.5


Tie(percent) 1.0 1.1 1.1 1.1

Failures 122

Nonfailures 12,266

1992


Intercept 0.5121) 0.4550) 0.2586) 0.5875)

(0.0166) (0.0242) (0.2099) (0.0057)

Leverage ratio -87.2859) -7.2337)

(0.0001) (0.3267)


(0.0001) (0.0001)


tier1 (0.0001) (0.5221)

Pseudo-R2 0.0832) 0.0770) 0.0665) 0.0781)



Tie (percent) 1.6 4.1 4.1 4.1

Failures 114

Nonfailures 11,827

1993


Intercept -2.4270) 0.0234) -2.3277) 0.0534)

(0.0001) (0.9416) (0.0001) (0.8761)

Leverageratio -40.6257) 2.4996)

(0.0001) (0.3609)


(0.0001) (0.0001)


tier1 (0.0001) (0.2988)

Pseudo-R2 0.0192) 0.0290) 0.0157) 0.0293)



Tie(percent) 3.8 5.0 2.8 5.0Failures 42

Nonfailures 11,431

Sources:FederalFinancialInstitutions ExaminationCouncil,ConsolidatedReports ofConditionandIncome;BoardofGovernors oftheFederalReserve


Notes:Numbers inparentheses are p-values.Pseudo-R2is definedin endnote 9.See alsoEstrella(1998).


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Thisregressionfindingprovidesevidencethatthegross

revenueratiocaneffectively supplementmorecomplicated

capitalratios.

Thus far,wehavefocusedonthecapacityofthecapital

measures topredictfailureover shortertimehorizons.One

wouldexpectthattheefficacyoftheseregulatorycapitalratios

mightdeteriorateifweevaluatetheirforecasting abilitybeyond

theone-ortwo-yearhorizon.PeekandRosengren(1997)

pointoutthatmostbanksthatfailedduringtheNewEngland

banking crisis of1989-93werewellcapitalizedtwoyearsbefore

failure.Similarly,Jones andKing (1995)arguethatbetween

1984and1989mosttroubledbanks wouldnothavebeen

classifiedas undercapitalizedunderthe FDICIArules.Those

studies suggestthatpromptcorrectiveactionrulesmandated

by FDICIAwouldhavebeenineffectiveindealing withbanking

problems during thoseperiods.

Table10

LogitRegressions

Dependent Variable: Failure betweenOne andTwoYears

1990


Intercept -0.1870) -0.4087) -0.5030) -0.2442)

(0.2954) (0.0177) (0.0034) (0.1774)

Leverageratio -62.1593) -22.2474)

(0.0001) (0.0437)


(0.0001) (0.4567)


tier1 (0.0001) (0.0001)

Pseudo-R2 0.0437) 0.0425) 0.0449) 0.0466)



Tie(percent) 2.9 2.8 2.6 2.4

Failures 167

Nonfailures 12,550

1991


Intercept -0.9504) -0.6484) -0.9654) -0.6917)

(0.0001) (0.0010) (0.0001) (0.0007)

Leverage ratio -50.6460) 18.8294)

(0.0001) (0.0001)

Gross revenueratio -5.9608) -4.6201

-0.0001) (0.0001)


tier1 (0.0001) (0.0002)

Pseudo-R2 0.0191) 0.0278) 0.0252) 0.0299)



Tie(percent) 3.0 3.2 2.2 3.2

Failures 125

Nonfailures 12,205

1992


Intercept -0.6818) -0.8511) -0.5561) -0.6623)

(0.0016) (0.0001) (0.0079) (0.0027)

Leverage ratio -56.1702) 19.9661)

(0.0001) (0.0805)


(0.0001) (0.5797)


tier1 (0.0001) (0.0001)

Pseudo-R2 0.0236) 0.0242) 0.0302) 0.0305)



Tie (percent) 2.6 2.9 2.4 3.1

Failures 119

Nonfailures 11,702

1993


Intercept -2.4512) -1.7406) -2.1743) -1.6986)

(0.0001) (0.0001) (0.0001) (0.0001)

Leverageratio -41.4685) 13.1137)

(0.0001) (0.0419)

Grossrevenue ratio -5.2671) -4.3610)

(0.0001) (0.0001)


tier1 (0.0001) (0.0741)

Pseudo-R2 0.0048) 0.0091) 0.0072) 0.0097)

Concordant(percent) 79.0 85.0 83.2 85.5Discordant(percent) 11.6 8.1 9.4 7.8

Tie (percent) 9.4 6.9 7.4 6.7

Failures 43

Nonfailures 11,292

Sources: Federal FinancialInstitutions ExaminationCouncil,ConsolidatedReports ofConditionandIncome;BoardofGovernors o fthe FederalReserve


Notes:Numbers inparentheses are p-values.Pseudo-R2is definedin endnote 9.See alsoEstrella(1998).


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-20

2

4

6

8

10

12

14

1618

0-1-2-3-4-5-6-7-8-9-10-11-12

Capital Ratios before Failure

Percent

Risk-Weighted Ratio

Sources: Federal Financial Institutions ExaminationCouncil,

Consolidated Reports ofConditionandIncome;BoardofGovernors

oftheFederal ReserveSystem,National InformationCenterdatabase;

authorscalculations.

Notes:The shadedarearepresents a1percentcritical regionofequality

forfailedand surviving banks.Whenthedashed lineis outsidethe

shadedarea,thepopulationmedianofsurviving banks is statistically

greaterthanthepopulationmedianoffailedbanks.

-2

0

2

4

6

8

10

0-1-2-3-4-5-6-7-8-9-10-11-12

Percent

Leverage Ra tio

-20

0

20

40

60

80

100

0-1-2-3-4-5-6-7-8-9-10-11-12

Percent

Gross Revenue Ratio

Cri tical region

Cri tical region

Cri tical region

Failed banks

Surviving bank s

Surviving bank s

Failed banks

Surviving bank s

Failed banks

Quarters before failure

Despitetheevidencethattheperformanceofcapitalratios

is not very goodatmoredistanthorizons,ouranalysis suggests

thatthesemeasures areactuallyabletodisseminateuseful

signalslongbeforetheeventoffailure. Forone,wefindthat

failing banks beginto show signs ofweakness (thatis,become

undercapitalized)twotothreeyears beforetheyareclosedby

supervisors.Thechartpresents thetime-profileofthethree

capitalratios forfailedbanks,plottedaccording tothenumber

ofquarters beforefailure.Thefigurealsoincludes analogous

measures foracontrol sampleofnonfailedbanks.Thecontrol

groupconsists ofrandomlychosenbanks locatedinthe same

stateandhavinganassetsizesimilartothatofthebanksinthe

failed group.

As thechart shows,themediancapitalratios forthe group

offailedbanks areconsistentlylowerthanthemedianratios for

thecontrol sampleofsurviving banks.The shadedareaineach

panelofthefigurerepresentsthecriticalregionforaone-sided

testofequality.Whenthemediancapitalratioforthecontrol

group(dashedline)is inthe shadedarea,wecannotrejectthe

hypothesisthatthemediancapitalratiosforthetwogroupsare

the sameatthe1percentlevel. Forthemostpart,themedian

capitalratioforthecontrol groupofnonfailedbanks is outside

the shadedcriticalregion, suggesting thatallthreecapitalratios

arefairly goodpredictors offailureevenas farbackas twoto

threeyears.

Another simplebutinteresting waytotestthelong-run

effectiveness ofthecapitalratios inpredicting failureis hazard

analysis.Althoughthehazardspecificationiscloselyrelatedto

binarymodels suchas logitorprobitmodels,itoffers abetter

waytoanalyzetheapparenttime-dependencyinthe

conditionalprobabilityoffailure.Morespecifically,thedependent variableinhazardanalysis is theprobabilitythatan

institutionwillfail giventhatithasnotfaileduntilthatpointof

time.10Thus,incontrasttothecross-sectionallogitmodelthat

examines failureover shorterhorizons,theproportional

hazardspecificationanalyzestheconditionallikelihoodfarther

intothefuture.To simplifyouranalysis,Table11examines two

scenarios ofsurvival.Thetoppanelofthetableevaluates the

efficacyofcapitalratiosinforecastingtheprobabilityoffailure

fromthefirstquarterof1988.Inthis case,theimplied

dependent variableis thedurationoftimefromthefirst

quarterof1988untilthebankfails oruntilthefourthquarter

of1993fornonfailingbanks (so-calledcensoredobservations).

Theexplanatory variables inthehazardmodels (models 1-4)

consistofthecompeting capitaladequacyratios as ofthefirst

quarterof1988.Thus,incontrasttotheyearlylogitregression,

whichestimatestheeffectivenessofcapitalratiosinforecasting

failurewithinoneyearorbetweenoneandtwoyears,the

hazardregressions evaluatetheearlywarning capacityofthe

capitalmeasuresfromthefirstquarterof1988.Toaccountfor

theeconomicdownturnin1990,thebottompanelofTable11

alsoestimates theprobabilityofbankfailurefromthefirst

quarterof1990.


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Endnotes


1.Ifbankspreferriskierassets(moralhazard),theymight choose

riskierborrowerswithinthehighestrisk-weightcategory.Thiseffect,

however,isunlikelytobe large enoughtooffsetthe primary effectof

reducingassetsinthehighestrisk-weightcategory.

2.Note thatthe proportionsoffailuresandnonfailuresare cumulated

inoppositeorders. Forinstance,the cumulativeproportionof

nonfailuresfortheleverageratioclassof2percentis0.5percent.This

proportionisthetotalnumberofsurvivingbanksuptoandincluding

that class(51+62+95=208),dividedbythe aggregate numberof

survivingbanks(43,643).Incontrast,thecumulativeproportionof

failuresforthissame leverage ratio classis33.0percent.This value is

equaltothecumulativenumberofbankfailuresforallbankswitha

leverage ratiogreaterthan2percent(76+45+31+25+17+8+3+2=131),

dividedby628,thetotalnumberoffailures.

3.Technically,thecriterionforcriticallyundercapitalizedbanksuses

tangibleequityasameasureofcapital,insteadoftier1,asinthe

leverageratio.Toeconomizeondatareportingandtomakeresults

more comparable withinthe article, we base ourillustrationson

Table 3, whichisbasedonthe leverage ratio.Tangible equityratios

producesimilarresults.

4.EqualityofTypeIandTypeIIerrorsisaninterestingillustrative

benchmark,butregulators can clearly choose differentlevelsofthis

trade-offtosuittheirgoalsandpreferences.

5.Tier2includesloan-lossreservesandanumberofconvertibleand

subordinateddebtinstruments.Banksare allowedtouse loan-loss

reservesuptoamaximumof1.25percentofrisk-weightedassets.

6.If istheestimatedproportion(failurerate),ameasureofthe

varianceoftheestimateisgivenby , where isthe

p

p 1 p( ) n n

numberofobservations.This variance islarger when is closerto

and issmaller,bothofwhichapplyinthecaseofsecond-yearrates

as compared withone-yearrates.

7.Early warningmodelsuse variousbalance-sheetandincome-

statementvariablestopredictbankfailure (see,for example,Cole,

Cornyn,andGunther[1995],ColeandGunther[1995],and

Thompson[1991]).Capitaladequacyishighlysignificantinthose

models.Nevertheless,highcorrelationamong variablesreflecting

financialstrengthmakesitdifficulttoinferthe significance of

individual variables.

8.Theconcordanceratioiscalculatedbasedonthepair-wise

comparisonoffailure probabilities estimatedbyalogitmodel.The

estimatedprobabilityforeachfailureiscomparedwiththosefor

nonfailure ( pairs whenthere are failuresoutof

observations).Apairiscountedasconcordantiftheestimated

probabilityishigherforthefailedoneanddiscordantintheopposite

case.Thus,ahighconcordanceratioindicatesthatthelogitmodel

accurately classifiesfailure andnonfailure.

9.Thepseudo-R2isdefinedasinEstrella(1998)by

,where isthe valueoftheuncon-

strainedlikelihood, isthe valueofthelikelihoodwithonlya

constantterminthemodel,and isthe numberofobservations.

10.Becau

seban

kfailur

e isaterm

in

al event,t

he p

r

ob

ab

ilityofb

an

kfailureattime giventhatithasnotfaileduntilthatpointintimeor

hazardrate is , where isthe

cumulativeprobabilityoffailureuptotime .Theproportional

hazardspecificationassumesthatthe hazardfunctionisseparable,

thatis, ,where isa vectorofexplanatory

variablesand isthe baseline hazardfunction.

p

n

m n m[ ] m n

1 Lulog Lclog( )2 Lclog n Lu

Lc

n

h x,( ) f x,( ) 1 F x,( )( )= F x,( )

h x,( ) h0 ( ) x[ ]exp= x

h0 ( )


20/20

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TheviewsexpressedinthispaperarethoseoftheauthorsanddonotnecessarilyreflectthepositionoftheFederalReserveBank

ofNewYork ortheFederalReserveSystem.TheFederalReserveBank ofNewYorkprovidesno warranty,expressor

implied,astotheaccuracy,timeliness,completeness,merchantability, orfitnessforanyparticularpurposeofany

informationcontainedindocumentsproducedandprovidedbytheFederalReserveBankofNewYorkinanyformor

manner whatsoever.

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